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1. Functions vear ALGEBRA & VECTOR ALGEBRA 1) Both A and R are true and R is the correct EXERCISE-I explanation of A 2) Both A and R are true but R is not correct 1. If f:(-6, 6]→R is defined by f(x)=x -3 explanation of A E R, then (fofo) (-1) + (fofoN(0) + (fofe)(1) = 1) f(4/2) 2) f(3/2) 3) f(2/2)4) f(/2) 3) A is true but R is flase 4) A is false but R is true 8. = 3 then the range of ab+bc+ca is Let X and Y be subsets of R, the set of all real numbers. The function f: X→Y defined by fx) = x for xɛ X ìs one-one but not onto if 2) X=R, Y=R* 2. 1) [-1/2,1] 2) [-1/2, ) -3 %3D 1) X=Y=R* .3 3) 2 4) [3, ∞ ) If f(X) = x-7 and g(x) 9 <x < 12, g(x) = 3) X=R*, Y=R 4) X=Y=R f(f(x)) then for 9. %3D 3. Let f and g be two real valued functions with 3) 14 - x 4) 7 – x domain A = {-2, 0, 2}. If ƒ = {(-2, 4), (0, 6), (2, 8)} and g = {(-2, –1), (0, 3), (2, 5)}, then 1) x – 14 2) x %3D %3D %3D 10. Let f:(-1, 1) → B , be a function defined by (2f), (3g) (3g) (2f) 2x (0) = f (x) = tan™ then f is both one-one .2 1-x 25 47 13 and onto when B is the interval 1) 12 2) - 12 3) 12 4) 12 TT TC TT TC TC 0, 2 If f: R→R and g : R→R are defined by 4) 2 2 4. 1) | 0, 2) 2 2 2. f(x)= 2x+3 and g(x)=x² +7, then values of ATIO 3) –1, –2 4) 1, -2 x such that g(f (x))=8 are 11. If f:C→C such that f(z) = z -ZVZE C, then 1) 1, 2 2) –1, 2 f is 1) one-one 2) onto 3) bijection If f(x)= px+q and g(x)=rx+s and Ag(x)] = g[f\x)] = 1) ƒ(p) = g(q) 3) ƒ(s)= g(q) 4) neither one one nor onto %3D 2х-1 , then f(y)=x gives k = 2) f(q)= g(q) 4) f(r)= g(p) 12. If y= f(x)= %3D X-k %3D 1) 2 2) -2 3) 1 4) –1 1 13. If fis an odd function and g is an even function, then fog is 6. If f: R→R is defined by f(x) = x - [x] - for xe R where [x] is the greatest integer not 1) even function 2) odd function exeeding x, then {xeR:f(x): 2. %3D 3) neither even nor odd 4) periodic function 1) Z, the set of all integers 14. If f(x) is a polynomial satisfying 2) N, the set of all natural numbers 3) Ø, the empty set f(x)s ==f(x)+ f and f(3) = 28 then f(4) = 4) R 1 %3D 7. A : fx) = log x and g(x) = 3 log x are equal 1) 63 2) 65 3) 67 4) 68 %3D functions e - e* +2 +e 15. The inverse of the function f (x): R: Two functions f and g are said to be equal if their domains and codomains are equal %3D et and f(x) = g(x) is given by %3D AKASH FAST TRACK CRD 5. 1. Functions vear ALGEBRA & VECTOR ALGEBRA 1) Both A and R are true and R is the correct EXERCISE-I explanation of A 2) Both A and R are true but R is not correct 1. If f:(-6, 6]→R is defined by f(x)=x -3 explanation of A E R, then (fofo) (-1) + (fofoN(0) + (fofe)(1) = 1) f(4/2) 2) f(3/2) 3) f(2/2)4) f(/2) 3) A is true but R is flase 4) A is false but R is true 8. = 3 then the range of ab+bc+ca is Let X and Y be subsets of R, the set of all real numbers. The function f: X→Y defined by fx) = x for xɛ X ìs one-one but not onto if 2) X=R, Y=R* 2. 1) [-1/2,1] 2) [-1/2, ) -3 %3D 1) X=Y=R* .3 3) 2 4) [3, ∞ ) If f(X) = x-7 and g(x) 9 <x < 12, g(x) = 3) X=R*, Y=R 4) X=Y=R f(f(x)) then for 9. %3D 3. Let f and g be two real valued functions with 3) 14 - x 4) 7 – x domain A = {-2, 0, 2}. If ƒ = {(-2, 4), (0, 6), (2, 8)} and g = {(-2, –1), (0, 3), (2, 5)}, then 1) x – 14 2) x %3D %3D %3D 10. Let f:(-1, 1) → B , be a function defined by (2f), (3g) (3g) (2f) 2x (0) = f (x) = tan™ then f is both one-one .2 1-x 25 47 13 and onto when B is the interval 1) 12 2) - 12 3) 12 4) 12 TT TC TT TC TC 0, 2 If f: R→R and g : R→R are defined by 4) 2 2 4. 1) | 0, 2) 2 2 2. f(x)= 2x+3 and g(x)=x² +7, then values of ATIO 3) –1, –2 4) 1, -2 x such that g(f (x))=8 are 11. If f:C→C such that f(z) = z -ZVZE C, then 1) 1, 2 2) –1, 2 f is 1) one-one 2) onto 3) bijection If f(x)= px+q and g(x)=rx+s and Ag(x)] = g[f\x)] = 1) ƒ(p) = g(q) 3) ƒ(s)= g(q) 4) neither one one nor onto %3D 2х-1 , then f(y)=x gives k = 2) f(q)= g(q) 4) f(r)= g(p) 12. If y= f(x)= %3D X-k %3D 1) 2 2) -2 3) 1 4) –1 1 13. If fis an odd function and g is an even function, then fog is 6. If f: R→R is defined by f(x) = x - [x] - for xe R where [x] is the greatest integer not 1) even function 2) odd function exeeding x, then {xeR:f(x): 2. %3D 3) neither even nor odd 4) periodic function 1) Z, the set of all integers 14. If f(x) is a polynomial satisfying 2) N, the set of all natural numbers 3) Ø, the empty set f(x)s ==f(x)+ f and f(3) = 28 then f(4) = 4) R 1 %3D 7. A : fx) = log x and g(x) = 3 log x are equal 1) 63 2) 65 3) 67 4) 68 %3D functions e - e* +2 +e 15. The inverse of the function f (x): R: Two functions f and g are said to be equal if their domains and codomains are equal %3D et and f(x) = g(x) is given by %3D AKASH FAST TRACK CRD 5.